Prediction procedure for the evaluation of interference between stations on the surface of the Earth at frequencies above about 0.

Transcription

1 Recommenation ITU-R P.45-6 (07/05) Preiction proceure for te evaluation of interference between stations on te surface of te Eart at frequencies above about 0. GHz P Series Raiowave propagation

2 ii Rec. ITU-R P.45-6 Forewor Te role of te Raiocommunication Sector is to ensure te rational, equitable, efficient an economical use of te raio-frequency spectrum by all raiocommunication services, incluing satellite services, an carry out stuies witout limit of frequency range on te basis of wic Recommenations are aopte. Te regulatory an policy functions of te Raiocommunication Sector are performe by Worl an Regional Raiocommunication Conferences an Raiocommunication Assemblies supporte by Stuy Groups. Policy on Intellectual Property Rigt (IPR) ITU-R policy on IPR is escribe in te Common Patent Policy for ITU-T/ITU-R/ISO/IEC reference in Annex of Resolution ITU-R. Forms to be use for te submission of patent statements an licensing eclarations by patent olers are available from ttp:// were te Guielines for Implementation of te Common Patent Policy for ITU-T/ITU-R/ISO/IEC an te ITU-R patent information atabase can also be foun. Series of ITU-R Recommenations (Also available online at ttp:// Series BO BR BS BT F M P RA RS S SA SF SM SNG TF V Title Satellite elivery Recoring for prouction, arcival an play-out; film for television Broacasting service (soun) Broacasting service (television) Fixe service Mobile, raioetermination, amateur an relate satellite services Raiowave propagation Raio astronomy Remote sensing systems Fixe-satellite service Space applications an meteorology Frequency saring an coorination between fixe-satellite an fixe service systems Spectrum management Satellite news gatering Time signals an frequency stanars emissions Vocabulary an relate subjects Note: Tis ITU-R Recommenation was approve in Englis uner te proceure etaile in Resolution ITU-R. Electronic Publication Geneva, 05 ITU 05 All rigts reserve. No part of tis publication may be reprouce, by any means watsoever, witout written permission of ITU.

3 Rec. ITU-R P.45-6 Scope RECOMMENDATION ITU-R P.45-6 * Preiction proceure for te evaluation of interference between stations on te surface of te Eart at frequencies above about 0. GHz (Question ITU-R 08/3) ( ) Tis Recommenation contains a preiction meto for te evaluation of interference between stations on te surface of te Eart at frequencies from about 0. GHz to 50 GHz, accounting for bot clear-air an yrometeor scattering interference mecanisms. Keywors Interference, Ducting, Troposperic scatter, Diffraction, Hyrometeor Scattering, Digital Data Proucts Te ITU Raiocommunication Assembly, consiering a) tat ue to congestion of te raio spectrum, frequency bans must be sare between ifferent terrestrial services, between systems in te same service an between systems in te terrestrial an Eart-space services; b) tat for te satisfactory coexistence of systems saring te same frequency bans, interference preiction proceures are neee tat are accurate an reliable in operation an acceptable to all parties concerne; c) tat propagation preictions are applie in interference preiction proceures wic are often require to meet worst-mont performance an availability objectives; ) tat preiction metos are require for application to all types of pat in all areas of te worl, recommens tat te interference preiction proceure given in Annex be use for te evaluation of te available propagation loss over unwante signal pats between stations on te surface of te Eart for frequencies above about 0. GHz. * Raiocommunication Stuy Group 3 mae eitorial amenments to tis Recommenation in 06 in accorance wit Resolution ITU-R.

4 Rec. ITU-R P.45-6 Annex Introuction Congestion of te raio-frequency spectrum as mae necessary te saring of many frequency bans between ifferent raio services, an between te ifferent operators of similar raio services. In orer to ensure te satisfactory coexistence of te terrestrial an Eart-space systems involve, it is important to be able to preict wit reasonable accuracy te interference potential between tem, using propagation preictions an moels wic are acceptable to all parties concerne, an wic ave emonstrate accuracy an reliability. Many types an combinations of interference pat may exist between stations on te surface of te Eart, an between tese stations an stations in space, an preiction metos are require for eac situation. Tis Annex aresses one of te more important sets of interference problems, i.e. tose situations were tere is a potential for interference between raio stations locate on te surface of te Eart. Te moels containe witin Recommenation ITU-R P.45 work from te assumption tat te interfering transmitter an te interfere-wit receiver bot operate witin te surface layer of atmospere. Use of exceptionally large antenna eigts to moel operations suc as aeronautical systems is not appropriate for tese moels. Te preiction proceure as been teste for raio stations operating in te frequency range of about 0. GHz to 50 GHz. Te moels witin Recommenation ITU-R P.45 are esigne to calculate propagation losses not exceee for time percentages over te range 0.00 p 50%. Tis assumption oes not imply te maximum loss will be at p = 50%. Te meto inclues a complementary set of propagation moels wic ensure tat te preictions embrace all te significant interference propagation mecanisms tat can arise. Metos for analysing te raio-meteorological an topograpical features of te pat are provie so tat preictions can be prepare for any practical interference pat falling witin te scope of te proceure up to a istance limit of km. Interference propagation mecanisms Interference may arise troug a range of propagation mecanisms wose iniviual ominance epens on climate, raio frequency, time percentage of interest, istance an pat topograpy. At any one time a single mecanism or more tan one may be present. Te principal interference propagation mecanisms are as follows: Line-of-sigt (Fig. ): Te most straigtforwar interference propagation situation is wen a line-of-sigt transmission pat exists uner normal (i.e. well-mixe) atmosperic conitions. However, an aitional complexity can come into play wen subpat iffraction causes a sligt increase in signal level above tat normally expecte. Also, on all but te sortest pats (i.e. pats longer tan about 5 km) signal levels can often be significantly enance for sort perios of time by multipat an focusing effects resulting from atmosperic stratification (see Fig. ). Diffraction (Fig. ): Beyon line-of-sigt (LoS) an uner normal conitions, iffraction effects generally ominate werever significant signal levels are to be foun. For services were anomalous sort-term problems are not important, te accuracy to wic iffraction can be moelle generally etermines te ensity of systems tat can be acieve. Te iffraction preiction capability must ave sufficient utility to cover smoot-eart, iscrete obstacle an irregular (unstructure) terrain situations.

5 Rec. ITU-R P Troposperic scatter (Fig. ): Tis mecanism efines te backgroun interference level for longer pats (e.g. more tan km) were te iffraction fiel becomes very weak. However, except for a few special cases involving sensitive receivers or very ig power interferers (e.g. raar systems), interference via troposcatter will be at too low a level to be significant. FIGURE Long-term interference propagation mecanisms Troposperic scatter Diffraction Line-of-sigt P Surface ucting (Fig. ): Tis is te most important sort-term propagation mecanism tat can cause interference over water an in flat coastal lan areas, an can give rise to ig signal levels over long istances (more tan 500 km over te sea). Suc signals can excee te equivalent free-space level uner certain conitions.

6 4 Rec. ITU-R P.45-6 FIGURE Anomalous (sort-term) interference propagation mecanisms Hyrometeor scatter Elevate layer reflection/refraction Ducting Line-of-sigt wit multipat enancements P Elevate layer reflection an refraction (Fig. ): Te treatment of reflection an/or refraction from layers at eigts up to a few unre metres is of major importance as tese mecanisms enable signals to overcome te iffraction loss of te terrain very effectively uner favourable pat geometry situations. Again te impact can be significant over quite long istances (up to km). Hyrometeor scatter (Fig. ): Hyrometeor scatter can be a potential source of interference between terrestrial link transmitters an eart stations because it may act virtually omniirectionally, an can terefore ave an impact off te great-circle interference pat. However, te interfering signal levels are quite low an o not usually represent a significant problem. A basic problem in interference preiction (wic is inee common to all troposperic preiction proceures) is te ifficulty of proviing a unifie consistent set of practical metos covering a wie range of istances an time percentages; i.e. for te real atmospere in wic te statistics of ominance by one mecanism merge graually into anoter as meteorological an/or pat conitions cange. Especially in tese transitional regions, a given level of signal may occur for a total time percentage wic is te sum of tose in ifferent mecanisms. Te approac in tis proceure as been to efine completely separate metos for clear-air an yrometeor-scatter interference preiction, as escribe in 4 an 5 respectively. Te clear-air meto consists of separate moels for iffraction, ucting/layer-reflection, an troposcatter. All tree are applie for every case, irrespective of weter a pat is LoS or transorizon. Te results are ten combine into an overall preiction using a blening tecnique tat ensures for any given pat istance an time percentage tat te signal enancement in te equivalent notional line-of-sigt moel is te igest attainable.

7 Rec. ITU-R P Clear-air interference preiction 3. General comments Altoug te clear-air meto is implemente by tree separate moels, te results of wic are ten blene, te proceure takes account of five basic types of propagation mecanism: line-of-sigt (incluing signal enancements ue to multipat an focusing effects); iffraction (embracing smoot-eart, irregular terrain an sub-pat cases); troposperic scatter; anomalous propagation (ucting an layer reflection/refraction); eigt-gain variation in clutter (were relevant). 3. Deriving a preiction 3.. Outline of te proceure Te steps require to acieve a preiction are as follows: Step : Input ata Te basic input ata require for te proceure is given in Table. All oter information require is erive from tese basic ata uring te execution of te proceure. TABLE Basic input ata Parameter Preferre resolution Description f 0.0 Frequency (GHz) p 0.00 Require time percentage(s) for wic te calculate basic transmission loss is not exceee φ t, φ r 0.00 Latitue of station (egrees) ψ t, ψ r 0.00 Longitue of station (egrees) tg, rg Antenna centre eigt above groun level (m) ts, rs Antenna centre eigt above mean sea level (m) G t, G r 0. Antenna gain in te irection of te orizon along te greatcircle interference pat (Bi) Pol N/A Signal, e.g. vertical or orizontal NOTE For te interfering an interfere-wit stations: t : interferer r : interfere-wit station. Polarization in Table is not a parameter wit a numerical value. Te information is use in 4... in connection wit equations (30a), (30b) an (3). Step : Selecting average year or worst-mont preiction Te coice of annual or worst-mont preictions is generally ictate by te quality (i.e. performance an availability) objectives of te interfere-wit raio system at te receiving en of te interference pat. As interference is often a biirectional problem, two suc sets of quality objectives may nee to be evaluate in orer to etermine te worst-case irection upon

8 6 Rec. ITU-R P.45-6 wic te minimum permissible basic transmission loss nees to be base. In te majority of cases te quality objectives will be couce in terms of a percentage of any mont, an ence worst-mont ata will be neee. Te propagation preiction moels preict te annual istribution of basic transmission loss. For average year preictions te percentages of time p, for wic particular values of basic transmission loss are not exceee, are use irectly in te preiction proceure. If average worst-mont preictions are require, te annual equivalent time percentage, p, of te worst-mont time percentage, pw, must be calculate for te pat centre latitue φ using: log( p ) log( ) 0.86ω w G L ω p 0 % () ω : fraction of te pat over water (see Table 3). G L.. cos cos for for (a) If necessary te value of p must be limite suc tat p pw. Note tat te latitue φ (egrees) is eeme to be positive in te Nortern Hemispere. Te calculate result will ten represent te basic transmission loss for te require worst-mont time percentage, pw%. Step 3: Raiometeorological ata Te preiction proceure employs tree raio-meteorological parameters to escribe te variability of backgroun an anomalous propagation conitions at te ifferent locations aroun te worl. ΔN (N-units/km), te average raio-refractive inex lapse-rate troug te lowest km of te atmospere, provies te ata upon wic te appropriate effective Eart raius can be calculate for pat profile an iffraction obstacle analysis. Note tat ΔN is a positive quantity in tis proceure. β0 (%), te time percentage for wic refractive inex lapse-rates exceeing 00 N-units/km can be expecte in te first 00 m of te lower atmospere, is use to estimate te relative incience of fully evelope anomalous propagation at te latitue uner consieration. Te value of 0 to be use is tat appropriate to te pat centre latitue. N0 (N-units), te sea-level surface refractivity, is use only by te troposcatter moel as a measure of location variability of te troposcatter scatter mecanism. As te scatter pat calculation is base on a pat geometry etermine by annual or worst-mont values of ΔN, tere is no aitional nee for worst-mont values of N0. Te correct values of ΔN an N0 are given by te pat-centre values as erive from te appropriate maps. Point incience of anomalous propagation, β0 (%), for te pat centre location is etermine using: μ μ % for 70 β 4 0 () 4.7μ μ4 % for 70

9 Rec. ITU-R P : pat centre latitue (egrees). Te parameter μ epens on te egree to wic te pat is over lan (inlan an/or coastal) an water, an is given by: tm τ μ 0 0 were te value of μ sall be limite to μ, wit: tm: lm: τ e ( ) (3).4 lm (3a) longest continuous lan (inlan + coastal) section of te great-circle pat (km) longest continuous inlan section of te great-circle pat (km). Te raioclimatic zones to be use for te erivation of tm an lm are efine in Table. ( ) log μ 0 for 70 μ4 (4) 0.3 log μ 0 for 70 TABLE Raio-climatic zones Zone type Coe Definition Coastal lan A Coastal lan an sore areas, i.e. lan ajacent to te sea up to an altitue of 00 m relative to mean sea or water level, but limite to a istance of 50 km from te nearest sea area. Were precise 00 m ata are not available an approximate value, i.e. 300 ft, may be use Inlan A All lan, oter tan coastal an sore areas efine as coastal lan above Sea B Seas, oceans an oter large boies of water (i.e. covering a circle of at least 00 km in iameter) Large boies of inlan water A large boy of inlan water, to be consiere as lying in Zone B, is efine as one aving an area of at least km, but excluing te area of rivers. Islans witin suc boies of water are to be inclue as water witin te calculation of tis area if tey ave elevations lower tan 00 m above te mean water level for more tan 90% of teir area. Islans tat o not meet tese criteria soul be classifie as lan for te purposes of te water area calculation. Large inlan lake or wet-lan areas Large inlan areas of greater tan km wic contain many small lakes or a river network soul be eclare as coastal Zone A by aministrations if te area comprises more tan 50% water, an more tan 90% of te lan is less tan 00 m above te mean water level.

10 8 Rec. ITU-R P.45-6 Climatic regions pertaining to Zone A, large inlan boies of water an large inlan lake an wetlan regions, are ifficult to etermine unambiguously. Terefore aministrations are invite to register wit te ITU Raiocommunication Bureau (BR) tose regions witin teir territorial bounaries tat tey wis ientifie as belonging to one of tese categories. In te absence of registere information to te contrary, all lan areas will be consiere too pertain to climate Zone A. For maximum consistency of results between aministrations te calculations of tis proceure soul be base on te ITU Digitize Worl Map (IDWM) wic is available from te BR. If all points on te pat are at least 50 km from te sea or oter large boies of water, ten only te inlan category applies. If te zone information is store in successive points along te raio pat, it soul be assume tat canges occur miway between points aving ifferent zone coes. Effective Eart raius Te meian effective Eart raius factor k50 for te pat is etermine using: 57 k50 (5) 57 N Assuming a true Eart raius of 6 37 km, te meian value of effective Eart raius ae can be etermine from: Te effective Eart raius exceee for 0% time, a, is given by: ae = 6 37 k50 km (6a) a = 6 37 k km (6b) were k = 3.0 is an estimate of te effective Eart raius factor exceee for 0% time. A general effective eart raius, ap, will be set to ae for 50% time an to a for 0% time in 4.. an 4... Step 4: Pat profile analysis Values for a number of pat-relate parameters necessary for te calculations, as inicate in Table 3, must be erive via an initial analysis of te pat profile base on te value of ae given by equation (6a). Information on te erivation, construction an analysis of te pat profile is given in Attacment to Annex.

11 Rec. ITU-R P TABLE 3 Parameter values to be erive from te pat profile analysis Parameter lt, lr θ t, θ r θ ts, rs te, re b ω ct,cr Great-circle pat istance (km) Description For a transorizon pat, istance from te transmit an receive antennas to teir respective orizons (km). For a LoS pat, eac is set to te istance from te terminal to te profile point ientifie as te Bullington point in te iffraction meto for 50% time For a transorizon pat, transmit an receive orizon elevation angles respectively (mra). For a LoS pat, eac is set to te elevation angle to te oter terminal Pat angular istance (mra) Antenna centre eigt above mean sea level (m) Effective eigts of antennas above te terrain (m) (see Attacment for efinitions) Aggregate lengt of te pat sections over water (km) Fraction of te total pat over water: ω = b / (7) were is te great-circle istance (km) calculate using equation (48). For totally overlan pats: ω = 0 Distance over lan from te transmit an receive antennas to te coast along te greatcircle interference pat (km). Set to zero for a terminal on a sip or sea platform 4 Clear-air propagation moels Basic transmission loss, Lb (B), not exceee for te require annual percentage time, p, is evaluate as escribe in te following sub-sections. 4. Line-of-sigt propagation (incluing sort-term effects) Te following soul be evaluate for bot LoS an transorizon pats. Basic transmission loss ue to free-space propagation an attenuation by atmosperic gases: Lbfsg = log f + 0 log + Ag B (8) Ag : γo, γw(ρ) : ρ : ω : total gaseous absorption (B): A g γ γ (ρ) B (9) o w specific attenuation ue to ry air an water vapour, respectively, an are foun from te equations in Recommenation ITU-R P.676 water vapour ensity: ω g/m 3 (9a) fraction of te total pat over water.

12 0 Rec. ITU-R P.45-6 Corrections for multipat an focusing effects at p an 0 percentage times: Esp =.6 [ exp( 0. {lt + lr})] log (p/50) B (0a) Es =.6 [ exp( 0. {lt + lr})] log (0/50) B (0b) Basic transmission loss not exceee for time percentage, p%, ue to LoS propagation: Lb0p = Lbfsg + Esp B () Basic transmission loss not exceee for time percentage, 0%, ue to LoS propagation: 4. Diffraction Lb0 = Lbfsg + Es B () Te time variability of te excess loss ue to te iffraction mecanism is assume to be te result of canges in bulk atmosperic raio refractivity lapse rate, i.e. as te time percentage p reuces, te effective Eart raius factor k ( p) is assume to increase. Tis process is consiere vali for β0 p 50%. For time percentages less tan β0 signal levels are ominate by anomalous propagation mecanisms rater tan by te bulk refractivity caracteristics of te atmospere. Tus iffraction loss not exceee for p < β0% is assume to be te same as for p β0% time. Taking tis into account, in te general case were p < 50%, te iffraction calculation must be performe twice, first for te meian effective Eart-raius factor k50 (equation (5)) an secon for te limiting effective Eart-raius factor kβ equal to 3. Tis secon calculation gives an estimate of iffraction loss not exceee for β0% time, were β0 is given by equation (). Te iffraction loss Lp not exceee for p% time, for 0.00% p 50%, is ten calculate using a limiting or interpolation proceure escribe in Te iffraction moel calculates te following quantities require in 4.6: Lp: Lb50: Lb: iffraction loss not exceee for p% time meian basic transmission loss associate wit iffraction basic transmission loss associate wit iffraction not exceee for p% time. Te iffraction loss is calculate by te combination of a meto base on te Bullington construction an sperical-eart iffraction. Te Bullington part of te meto is an expansion of te basic Bullington construction to control te transition between free-space an obstructe conitions. Tis part of te meto is use twice: for te actual pat profile, an for a zero-eigt smoot profile wit moifie antenna eigts referre to as effective antenna eigts. Te same effective antenna eigts are also use to calculate te sperical-eart iffraction loss. Te final result is obtaine as a combination of tree losses calculate as above. For a perfectly smoot pat, te final iffraction loss will be te output of te sperical-eart moel. Tis meto provies an estimate of iffraction loss for all types of pats, incluing over-sea or over-inlan or coastal lan, an irrespective of weter te lan is smoot or roug, an weter LoS or transorizon. Tis meto also makes extensive use of an approximation to te single knife-ege iffraction loss as a function of te imensionless parameter,, given by: J ( ) 6.9 0log Note tat J( 0.78) 0, an tis efines te lower limit at wic tis approximation soul be use. J(ν) is set to zero for ν < (3)

13 Rec. ITU-R P.45-6 Te overall iffraction calculation is escribe in te subsections as follows: 4.. escribes te Bullington part of te iffraction meto. For eac iffraction calculation for a given effective Eart raius tis is use twice. On te secon occasion, te antenna eigts are moifie an all profile eigts are zero. 4.. escribes te sperical-eart part of te iffraction moel. Tis is use wit te same antenna eigts as for te secon use of te Bullington part in escribes ow te metos in 4.. an 4.. are use in combination to perform te complete iffraction calculation for a given effective Eart raius. Due to te manner in wic te Bullington an sperical-eart parts are use, te complete calculation as come to be known as te elta-bullington moel escribes te complete calculation for iffraction loss not exceee for a given percentage time p%. 4.. Te Bullington part of te iffraction calculation In te following equations, slopes are calculate in m/km relative to te baseline joining sea level at te transmitter to sea level at te receiver. Te istance an eigt of te i-t profile point are i kilometres an i metres above mean sea level respectively, i takes values from 0 to n were n + is te number of profile points, an te complete pat lengt is kilometres. For convenience te terminals at te start an en of te profile are referre to as transmitter an receiver, wit eigts in m above sea level, ts an rs, respectively. Effective Eart curvature Ce km is given by /ap were ap is effective eart raius in kilometres. Wavelengt in metres is represente by. Fin te intermeiate profile point wit te igest slope of te line from te transmitter to te point. S tim were te profile inex i takes values from to n. i 500C ei i ts max m/km (4) Calculate te slope of te line from transmitter to receiver assuming a LoS pat: Two cases must now be consiere. Case. Pat is LoS If Stim < Str te pat is LoS. S tr rs i ts m/km (5) Fin te intermeiate profile point wit te igest iffraction parameter : ts i rsi max max i 500Cei i (6) were te profile inex i takes values from to n. In tis case, te knife-ege loss for te Bullington point is given by: Luc max J B (7) were te function J is given by equation (3) for b greater tan 0.78, an is zero oterwise. Case. Pat is transorizon If Stim Str te pat is transorizon. Fin te intermeiate profile point wit te igest slope of te line from te receiver to te point. i i

14 Rec. ITU-R P.45-6 S rim were te profile inex i takes values from to n. i 500Cei i rs max m/km (8) i Calculate te istance of te Bullington point from te transmitter: bp S Calculate te iffraction parameter, b, for te Bullington point rs ts rim Stim S km (9) rim ts bp rsbp 0.00 b ts Stimbp In tis case, te knife-ege loss for te Bullington point is given by: L uc b bp bp (0) J B () For Luc calculate using eiter equation (7) or (), Bullington iffraction loss for te pat is now given by: 4.. Sperical-Eart iffraction loss Lbull = Luc + [ exp( Luc/6)](0+0.0 ) B () Te sperical-eart iffraction loss not exceee for p% time for antenna eigts te an re (m), Lsp, is calculate as follows. Calculate te marginal LoS istance for a smoot pat: los p a km (3) If los calculate iffraction loss using te meto in 4... below for aft = ap to give Lft, an set Lsp equal to Lft. No furter sperical-eart iffraction calculation is necessary. Oterwise continue as follows: Calculate te smallest clearance eigt between te curve-eart pat an te ray between te antennas, se, given by: te re se se se se te 500 re 500 se a p a p m (4) ( ) km (5a) se b km (5b) se se m 3c 3m b cos arccos 3m ( m ) were te arccos function returns an angle in raians. te re (5c) te re c (5)

15 Rec. ITU-R P Calculate te require clearance for zero iffraction loss, req, given by: req m 50 (5e) a ( ) p te re se se m (6) If se > req te sperical-eart iffraction loss Lsp is zero. No furter sperical-eart iffraction calculation is necessary. Oterwise continue as follows: Calculate te moifie effective eart raius, aem, wic gives marginal LoS at istance given by: Use te meto in 4... for aft = aem to give Lft. 500 a em km (7) te re If Lft is negative, te sperical-eart iffraction loss, Lsp, is zero, an no furter sperical-eart iffraction calculation is necessary. Oterwise continue as follows: Calculate te sperical-eart iffraction loss by interpolation: sp se req L ft 4... First-term part of sperical-eart iffraction loss L / B (8) Tis sub-section gives te meto for calculating sperical-eart iffraction using only te first term of te resiue series. It forms part of te overall iffraction meto escribe in 4.. above to give te first-term iffraction loss, Lft, for a given value of effective Eart raius aft. Te value of aft to use is given in 4... Set terrain electrical properties typical for lan, wit relative permittivity r.0 an conuctivity S/m an calculate Lft using equations (30) to (37) an call te result Lftlan. Set terrain electrical properties typical for sea, wit relative permittivity r an conuctivity 5.0 S/m an calculate Lft using equations (30) to (37) an call te result Lftsea. First-term sperical iffraction loss is now given by: L L ( ) L B (9) ft ftsea ftlan were is te fraction of te pat over sea. Start of calculation to be performe twice, as escribe above: Normalize factor for surface amittance for orizontal an vertical polarization. an: /3 r KH aft f ( ) (8 / f ) /4 (orizontal) (30a)

16 4 Rec. ITU-R P.45-6 K K f V H r (8 / ) / (vertical) (30b) If te polarization vector contains bot orizontal an vertical components, e.g. circular or slant, ecompose it into orizontal an vertical components, calculate eac separately starting from equations (30a) an (30b) an combine te results by a vector sum of te fiel amplitue. In practice tis ecomposition will generally be unnecessary because above 300 MHz a value of can be use for βft in equation (3). Calculate te Eart groun/polarization parameter: were K is KH or KV accoring to polarization. Normalize istance: Normalize transmitter an receiver eigts: Calculate te istance term given by: Y Y 4.6K 0.67K ft (3) 4 4.5K.53K X t r /3 f.88 β ft (3) a ft /3 f β ft te (33a) a ft /3 f β ft re (33b) a ft 0 log( X ) 7.6X for X.6 F X.45 (34) 0 log( X ) X for X.6 Define a function of normalize eigt given by: ( B.) 5log(.) 8 for > ( ) t / r Bt / r B G Y t/r t / r 3 (35) 0 log( Bt / r 0.Bt / r ) oterwise B B t r Y (36a) ft t Y (36b) ft r If G(Y) is less tan + 0logK, ten limit G(Y) suc tat G( Y) 0log K. Te first-term sperical-eart iffraction loss is now given by: L ft X GY 4..3 Complete elta-bullington iffraction loss moel F G Y B (37) Use te meto in 4.. for te actual terrain profile an antenna eigts. Set te resulting Bullington iffraction loss for te actual pat, Lbulla=Lbull as given by equation (). t r

17 Rec. ITU-R P Use te meto in 4.. for a secon time, wit all profile eigts, i, set to zero, an moifie antenna eigts given by: ' ts ts st masl (38a) ' rs rs sr masl (38b) were te smoot-eart eigts at transmitter an receiver, st an sr, are given in of Attacment. Set te resulting Bullington iffraction loss for tis smoot pat, Lbulls=Lbull as given by equation (). Use te meto in 4.. to calculate te sperical-eart iffraction loss Lsp for te actual pat lengt (km) an wit: Diffraction loss for te general pat is now given by: L ' te ts m (39a) ' re rs m (39b) L max{ L Lbulls, 0} B (40) bulla sp 4..4 Te iffraction loss not exceee for p% of te time Use te meto in 4..3 to calculate iffraction loss L for effective Eart raius ap=ae as given by equation (6a). Set meian iffraction loss L50 = L. If p = 50% te iffraction loss not exceee for p% time, Lp, is given by L50, an tis completes te iffraction calculation. If p < 50% continue as follows. Use te meto in 4..3 to calculate iffraction loss L for effective Eart raius ap=a as given in equation (6b). Set iffraction loss not exceee for β0% time Lβ = L. Te application of te two possible values of effective Eart raius factor is controlle by an interpolation factor, Fi, base on te normal istribution of iffraction loss over te range β0% p < 50% given by: Fi = p I 00 0 I 00 for 50% > p > β0% (4a) = for β0% p (4b) were I(x) is te inverse complementary cumulative normal function. An approximation for I(x) wic may be use wit confience for x < 0.5 is given in Attacment 3 to Annex. Te iffraction loss, Lp, not exceee for p% time, is now given by: Lp = L50 + Fi (L L50) B (4) were L50 an L are efine above, an Fi is efine by equations (4a) an (4b), epening on te values of p an 0. Te meian basic transmission loss associate wit iffraction, Lb50, is given by: Lb50 = Lbfsg + L50 B (43)

18 6 Rec. ITU-R P.45-6 were Lbfsg is given by equation (8). Te basic transmission loss associate wit iffraction not exceee for p% time is given by: were Lb0p is given by equation (). 4.3 Troposperic scatter (Notes an ) Lb = Lb0p + Lp B (44) NOTE At time percentages muc below 50%, it is ifficult to separate te true troposperic scatter moe from oter seconary propagation penomena wic give rise to similar propagation effects. Te troposperic scatter moel aopte in tis Recommenation is terefore an empirical generalization of te concept of troposperic scatter wic also embraces tese seconary propagation effects. Tis allows a continuous consistent preiction of basic transmission loss over te range of time percentages p from 0.00% to 50%, tus linking te ucting an layer reflection moel at te small time percentages wit te true scatter moe appropriate to te weak resiual fiel exceee for te largest time percentage. NOTE Tis troposcatter preiction moel as been erive for interference preiction purposes an is not appropriate for te calculation of propagation conitions above 50% of time affecting te performance aspects of trans-orizon raio-relay systems. Te basic transmission loss ue to troposcatter, Lbs (B) not exceee for any time percentage, p, below 50%, is given by: L bs log ( / L 0 log θ 0.5 N p B (45) Lf: Lc: f frequency epenent loss: 0 Lc Ag 0. ) Lf = 5 log f.5 [log ( f / )] B (45a) aperture to meium coupling loss (B): L c 0.055( G ) 0.05 e t G r B (45b) N0 : pat centre sea-level surface refractivity erive from Fig. 6 Ag : 4.4 Ducting/layer reflection gaseous absorption erive from equation (9) using ρ = 3 g/m 3 for te wole pat lengt. Te preiction of te basic transmission loss, Lba (B) occurring uring perios of anomalous propagation (ucting an layer reflection) is base on te following function: Af : Lba = Af + A ( p) + Ag B (46) total of fixe coupling losses (except for local clutter losses) between te antennas an te anomalous propagation structure witin te atmospere: Af = log f + 0 log(lt + lr) + Alf + Ast + Asr + Act + Acr B (47) Alf: Ast, Asr : empirical correction to account for te increasing attenuation wit wavelengt inucte propagation Alf(f) = f f B if f < 0.5 GHz (47a) Alf(f) = 0.0 B oterwise site-sieling iffraction losses for te interfering an interfere-wit stations respectively:

19 Rec. ITU-R P / / 3 0log 0.36 t, r f lt,lr 0.64 t, r f B for t, r 0 mra A (48) st, sr 0 B for t, r 0 mra Act, Acr: θ 0. mra (48a) t, r t,r lt,lr over-sea surface uct coupling corrections for te interfering an interferewit stations respectively: e ct,cr Act,cr tan (0.07(50 ts,rs )) B for 0.75 ct,cr lt,lr (49) ct,cr 5 km A ct, cr 0 B for all oter conitions (49a) It is useful to note te limite set of conitions uner wic equation (49) is neee. A( p) : γ : θ' : time percentage an angular-istance epenent losses witin te anomalous propagation mecanism: specific attenuation: A ( p) = γ θ + A ( p) B (50) γ = ae f /3 B/mra (5) angular istance (correcte were appropriate (via equation (5a)) to allow for te application of te site sieling moel in equation (48)): t, r mra (5) θt,r t r a e lt,lr for for θ θ t,r t,r A( p) : time percentage variability (cumulative istribution): lt,lr lt,lr mra mra (5a) 3 p p A ( p) ( ) log B (53) β β log 0.98(log) e.0 (53a).0058 log β β = β0 μ μ3 % (54) Γ

20 8 Rec. ITU-R P.45-6 μ: correction for pat geometry: 500 ae te re (55) Te value of μ sall not excee τ (55a) = 3.5 : is efine in equation (3a) an te value of sall not be allowe to reuce below 3.4. μ3 : correction for terrain rougness: 3 Ag: exp ( m 0) (43 6 I ) for for m m 0 m 0 m (56) I = min ( lt lr, 40) km (56a) total gaseous absorption etermine from equations (9) an (9a). Te remaining terms ave been efine in Tables an an Attacment. 4.5 Aitional clutter losses 4.5. General Consierable benefit, in terms of protection from interference, can be erive from te aitional iffraction losses available to antennas wic are imbee in local groun clutter (builings, vegetation, etc.). Tis proceure allows for te aition of suc clutter losses at eiter or bot ens of te pat in situations were te clutter scenario is known. It preicts a maximum aitional loss at eiter en of te pat, applie via an S-sape interpolation function intene to avoi an overestimate of te sieling loss. Te maximum aitional loss is 0 B above 0.9 GHz, an progressively less at lower frequencies, own to 5 B at 0. GHz. Were tere are oubts as to te certainty of te clutter environment tis aitional loss soul not be inclue. Were te correction is use, care soul be taken not to expect ig clutter losses in a ig-rise urban area consisting of isolate tall builings separate by open spaces. Lower clutter losses are often observe in suc areas compare to more traitional city centres comprising lower but more connecte blocks of builings. Te clutter losses are esignate as At (B) an Ar (B) for te interferer an interfere-wit stations respectively. Te aitional protection available is eigt epenent, an is terefore moelle by a eigt-gain function normalize to te nominal eigt of te clutter. Appropriate nominal eigts are available for a range of clutter types. Te correction applies to all clear-air preictions in tis Recommenation, i.e. for all propagation moes an time percentages.

21 Rec. ITU-R P Clutter categories Table 4 inicates te clutter (or groun cover) categories as efine in Recommenation ITU-R P.058 for wic te eigt-gain correction can be applie. Te nominal clutter eigt, a (m) an istance from te antenna, k (km) are eeme to be average values most representative of te clutter type. However, te correction moel as been mae conservative in recognition of te uncertainties over te actual eigt tat are appropriate in iniviual situations. Were te clutter parameters are more accurately known tey can be irectly substitute for te values taken from Table 4. Te nominal eigts an istances given in Table 4 approximate to te caracteristic eigt Hc an gap-wit Gc efine in Recommenation ITU-R P.058. However te moel use ere to estimate te aitional losses ue to sieling by clutter (groun cover) is intene to be conservative Te eigt-gain moel Te aitional loss ue to protection from local clutter is given by te expression: an: A 0.5 F e k fc tan B (57) a F fc tan 7.5 f 0.5 (57a) k : istance (km) from nominal clutter point to te antenna (see Fig. 3) : antenna eigt (m) above local groun level a : nominal clutter eigt (m) above local groun level. Clutter (groun-cover) category TABLE 4 Nominal clutter eigts an istances Nominal eigt, a (m) Nominal istance, k (km) Hig crop fiels Park lan 4 0. Irregularly space sparse trees Orcar (regularly space) Sparse ouses Village centre Deciuous trees (irregularly space) Deciuous trees (regularly space) Mixe tree forest

22 0 Rec. ITU-R P.45-6 Clutter (groun-cover) category TABLE 4 (en) Nominal eigt, a (m) Nominal istance, k (km) Coniferous trees (irregularly space) Coniferous trees (regularly space) Tropical rain forest Suburban Dense suburban 0.0 Urban Dense urban Hig-rise urban Inustrial zone Aitional losses ue to sieling by clutter (groun cover) soul not be claime for categories not appearing in Table 4. FIGURE 3 Meto of applying eigt-gain correction, At or Ar "Site sieling" obstacle * Nominal clutter eigt, (m) a Nominal groun eigt, (m) g Pat lengt, (km) s (km) L k Assume clutter istance(s), an (km) s k Nominal clutter location P Meto of application Te meto of applying te eigt-gain correction, At or Ar (B) is straigtforwar, an is sown in Fig. 3. Te steps to be ae to te basic preiction proceure are as follows: Step : Were te clutter type is known or can be safely assume, te main proceure is use to calculate te basic transmission loss to te nominal eigt, a, for te appropriate clutter type, as selecte from Table 4. Te pat lengt to be use is k (km). However were >> k tis minor correction for k can safely be ignore. Step : Were tere is a site-sieling obstacle tat will provie protection to te terminal tis soul still be inclue in te basic calculation, but te sieling loss (Ast or Asr (B)) soul be calculate to te eigt a at istance s, rater tan to at L as woul oterwise be te case.

23 Rec. ITU-R P.45-6 Step 3: Once te main proceure is complete, te eigt gain correction from equation (57) can be ae, as inicate in equation (64). Step 4: Were information on te clutter is not available, te basic calculation soul be unertaken using istances an L (if appropriate) an eigt. NOTE Clutter eigt-gain corrections soul be ae to bot ens of te pat were tis is appropriate. NOTE Were bot te lan eigt-gain correction an te sea uct coupling correction (A ct or A cr (B)) are require (i.e. te antenna is close to te sea but tere is intervening clutter), te two corrections can be use togeter as tey are complementary an compatible. NOTE 3 If is not significantly greater tan k tis moel is not suitable. 4.6 Te overall preiction Te following proceure soul be applie to te results of te foregoing calculations for all pats. Calculate an interpolation factor, Fj, to take account of te pat angular istance: Stim Str Fj tan 3. 0 (58) ξ: ajustable parameter currently set to 0.8 (Stim Str): slope parameters efine in equations (4) an (5) Θ: ajustable parameter currently set to 0.3 mra. Calculate an interpolation factor, Fk, to take account of te great circle pat istance: F k ( sw) tan 3.0 (59) sw : great circle pat lengt (km) (efine in Table 3) sw : κ : fixe parameter etermining te istance range of te associate blening, set to 0 fixe parameter etermining te blening slope at te ens of te range, set to 0.5 Calculate a notional minimum basic transmission loss, Lminb0p (B) associate wit LoS propagation an over-sea sub-pat iffraction. L min Lb0 p ( ) Lp for p 0 b 0 p B (60) Lb50 ( Lb0 ( ) Lp Lb50) Fi for p 0 Lb0p: Lb0 : notional LoS basic transmission loss not exceee for p% time, given by equation () notional LoS basic transmission loss not exceee for % time, given by equation () Lp : iffraction loss not exceee for p% time, calculate using te meto in 4.. Calculate a notional minimum basic transmission loss, Lminbap (B), associate wit LoS an transorizon signal enancements:

24 Rec. ITU-R P.45-6 Lba: Lb0p: η =.5. L minbap L L ba b0 p ln exp exp B (6) ucting/layer reflection basic transmission loss not exceee for p% time, given by equation (46) notional line-of-sigt basic transmission loss not exceee for p% time, given by equation () Calculate a notional basic transmission loss, Lba (B), associate wit iffraction an LoS or ucting/layer-reflection enancements: L ba L L Lb : b minbap ( L b L minbap ) F k for for L L minbap minbap L L b b B (6) basic transmission loss for iffraction not exceee for p% time from equation (44) Fk : interpolation factor given by equation (59) accoring to te values of p an 0. Calculate a moifie basic transmission loss, Lbam (B), wic takes iffraction an LoS or ucting/layer-reflection enancements into account: L ) bam Lba ( Lminb0 p Lba Fj B (63) Calculate te final basic transmission loss not excee for p% time, Lb (B), as given by: At,r: L b 0.L L bs 0. 0 bam At Ar 5 log 0 B (64) aitional losses to account for clutter sieling te transmitter an receiver. Tese soul be set to zero if tere is no suc sieling. 4.7 Calculation of transmission loss Te meto escribe in 4. to 4.6 above provies te basic transmission loss between te two stations. In orer to calculate te signal level at one station ue to interference from te oter it is necessary to know te transmission loss, wic takes account of te antenna gains of te two stations in te irection of te raio (i.e. interference) pat between tem. Te following proceure provies a meto for te calculation of transmission loss between two terrestrial stations. As intermeiate steps in te meto, it also provies formulae for te calculation of te great-circle pat lengt an angular istance base on te stations geograpic coorinates, as oppose to te erivations of tese quantities from te pat profile, as assume in Table 3. Calculate te angle subtene by te pat at te centre of te Eart, δ, from te stations geograpic coorinates using: δ = arccos(sin(φt) sin(φr) + cos(φt) cos(φr) cos(ψt ψr)) ra (65)

25 Rec. ITU-R P Te great circle istance,, between te stations is: = 6 37 δ km (66) Calculate te bearing (azimutal irection clockwise from true Nort) from station t to station r using: tr = arccos({sin(φr) sin(φt) cos(δ)}/sin(δ) cos(φt)) ra (67) Having implemente equation (67), if ψt ψr > 0 ten: tr = π tr ra (68) Calculate te bearing from station r to station t, rt, by symmetry from equations (67) an (68). Next, assume tat te main beam (boresigt) irection of station t is (εt, t) in (elevation, bearing), wile te main beam irection of station r is (εr, r). To obtain te elevation angles of te raio (i.e. interference) pat at stations t an r, εpt an εpr, respectively, it is necessary to istinguis between line-of-sigt an trans-orizon pats. For example, for line-of-sigt pats: an: r t pt ra (69a) a e t r pr ra (69b) a e were t an r are te eigts of te stations above mean sea level (km), wile for trans-orizon pats, te elevation angles are given by teir respective orizon angles: an: θ t pt ra (70a) 000 r pr ra (70b) 000 Note tat te raio orizon angles, θt an θr (mra), are first introuce in Table 3 an are efine in 5.. an 5..3, respectively, of Attacment to Annex. To calculate te off-boresigt angles for stations t an r, χ t an χ r, respectively, in te irection of te interference pat at stations t an r, it is recommene to use: an: χ t arccos(cos(εt) cos(εpt) cos(tr t) + sin(εt) sin(εpt)) r arccos(cos(εr) cos(εpr) cos(rt r) + sin(εr) sin(εpr)) (7a) (7b)

26 4 Rec. ITU-R P.45-6 Using teir respective off-boresigt angles, obtain te antenna gains for stations t an r, Gt an Gr, respectively (B). If te actual antenna raiation patterns are not available, te variation of gain wit off-boresigt angle may be obtaine from te information in Recommenation ITU-R S.465. To obtain te transmission loss, L, use: L = Lb ( p) Gt Gr B (7) For clear-air interference scenarios were raio propagation is ominate by troposcatter, te elevation angles will be sligtly greater tan te raio orizon angles, t an r. Te use of tese soul introuce negligible error, unless tese also coincie wit teir respective stations boresigt irections. 5 Hyrometeor-scatter interference preiction In contrast to te preceing clear-air preiction metos escribe above, te yrometeor-scatter interference preiction metoology escribe below evelops expressions for te transmission loss between two stations irectly, since it requires a knowlege of te interfering an victim antenna raiation patterns for eac station. Te meto is quite general, in tat it can be use wit any antenna raiation pattern wic provies a meto for etermining te antenna gain at any off-boresigt axis angle. Raiation patterns suc as tose in Recommenations ITU-R P.60, ITU-R F.699, ITU-R F.45, ITU-R S.465 an ITU-R S.580, for example, can all be use, as can more complex patterns base Bessel functions an actual measure patterns if tese are available. Te meto can also be use wit omniirectional or sectoral antennas, suc as tose caracterize in Recommenation ITU-R F.336, te gain of wic is generally etermine from te vertical off-boresigt axis angle (i.e. te elevation relative to te angle of maximum gain). Te meto is also general in tat it is not restricte to any particular geometry, provie tat antenna raiation patterns are available wit 80 coverage. Tus, it inclues bot main beam-to-main beam coupling an sie lobe-to-main beam coupling, an bot great-circle scatter an sie-scatter geometries. Te meto can compute interference levels for bot long-pat (> 00 km) an sort-pat geometries (own to a few kilometres) wit arbitrary elevation an azimutal angles at eiter station. Te metoology is terefore appropriate to a wie range of scenarios an services, incluing te etermination of rain-scatter interference between two terrestrial stations, between a terrestrial station an an eart station, an between two eart stations operating in biirectionally allocate frequency bans. 5. Introuction Te metoology is base on application of te bistatic raar equation, wic can be written in terms of te power Pr receive at a receiving station from scattering by rain of te power Pt transmitte by a transmitting station: : Gt : Gr : P P r t 3 4 all space GtGrA V r r wavelengt gain (linear) of te transmitting antenna gain (linear) of te receiving antenna t r W (73)

27 Rec. ITU-R P : scattering cross-section per unit volume, V (m /m 3 ) A : rt : rr : attenuation along te pat from transmitter to receiver (in linear terms) istance from te transmitter to te scattering volume element istance from te scattering volume element to te receiver. Expresse in terms of te transmission loss, (B), for scattering between two stations, Station an Station, te bistatic raar equation becomes: L 78 0log N 0 log f 0 log Z 0 log C 0 log S A M B (74) N: refractive inex epenent Rayleig Scattering term R g R 0log S 0 m N (74a) m m: complex refractive inex epening on frequency an atmosperic conitions f : ZR : frequency (GHz) raar reflectivity at groun level, wic can be expresse in terms of te rainfall rate, R (mm/):.4 Z R 400R (75) 0 log S: correction (B), to account for te eviation from Rayleig scattering at frequencies above 0 GHz: φs : Ag : M : 3 4 cos.6 S f 0 5 f 0 scattering angle.7 cos S for f 0 GHz for f 0 GHz (76) attenuation ue to atmosperic gases along te pat from transmitter to receiver (B), calculate from Recommenation ITU-R P.676 Annex any polarization mismatc between transmitting an receiving systems (B). In te moel given ere, scattering is confine to tat witin a rain cell, wic is efine as being of circular cross-section, wit a iameter epening on te rainfall rate: 0.08 c 3.3R km (77) Witin te rain cell, te rainfall rate, an ence te raar reflectivity, is assume to be constant up to te rain eigt, R. Above te rain eigt, te reflectivity is assume to ecrease linearly wit eigt at a rate of 6.5 B/km. Te scatter transfer function, C, is ten te volume integral over te rain cell an can be written, in cylinrical coorinates, as: C max 0 c 0 0 GG A r r (78) r r

28 6 Rec. ITU-R P.45-6 G,G : linear gains of Station an Station, respectively r, r : istances (km) from te integration element V to Station an Station, respectively A : : R : attenuation ue to rain, bot insie an outsie te rain cell, expresse in linear terms eigt epenence of te raar reflectivity: 0 rain eigt (km) 0.65( R ) for R for r, φ, : variables of integration witin te rain cell. Te integration is carrie out numerically, in cylinrical coorinates. However, it is convenient initially to consier te geometry of te scattering from te transmitting station troug a rain cell to te receiving station in terms of a Cartesian coorinate system wit Station taken as te origin, since te actual position of te rain cell will not immeiately be efine, especially in te case of sie scattering. Witin te Cartesian coorinate reference, it is avantageous, in terms of simplicity, first to convert te various geometrical parameters from teir actual curve-eart values to a plane-eart representation. Te existence of main beam-to-main beam coupling between te antennas is establise from te geometry, an te rain cell is ten locate at te point of intersection between te main beam axes. If main beam-to-main beam coupling oes not exist, ten te rain cell is locate along te main beam axis of Station, centre at te point of closest approac to te main beam axis of Station. In tis case, te transmission losses soul be etermine for a secon case wit te parameters of eac station intercange, an te worst-case loss istribution taken as representative of te likely interference levels. 5. Input parameters Table 5 lists all te input parameters wic are require for implementation of te meto to calculate te cumulative istribution of transmission loss between two stations ue to rain scatter. R (79)